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The figure above shows the dimensions of a rectangular board
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Updated on: 09 Jan 2014, 01:04

1

18

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

45%(02:49) correct 55%(03:07) wrong based on 336 sessions

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Attachment:

ps4.JPG [ 33.08 KiB | Viewed 11996 times ]

The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A, B, and C, as indicated. If x = 45, what is the length AB ? (1 foot = 12 inches)

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09 Nov 2010, 19:20

12

3

milind1979 wrote:

Attachment:

The attachment ps4.JPG is no longer available

The length of the rectangle is 240 inches. The diagram shows you the isosceles triangle whose side will be 6 inches. From 240, if we remove 2 of these sides of 6 inches each, we will be left with 228 inches.

Attachment:

Ques.jpg [ 8.15 KiB | Viewed 10617 times ]

This 228 inches has to be equally divided into 4 parts as shown by the blue arrows. Why are these parts equal? Because the question says that the four pieces are identical. So the smaller side of each piece has to be equal (Look at the blue line on the top. This should be equal to the blue lines at the bottom).

The length of each of the blue lines will be 228/4 = 57 inches.The length of AB = 57 + 6 inches = 63 inches.
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AB=AD+DBAD is 6 inches since x is 45 degrees.To obtain DB you have to subtract 2*6inces (6 inches because of AD and other 6inches more because CE=AD) to the long side (20 feet) and divide by 4 since there are 4 segments like DB.It´s quiet complicated to explain...

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10 Nov 2010, 09:20

1

Draw a perpendicular till point P on AB to make it right isosceles triangle- With principle of 45-45-90 you get AP=6.As Karishma told- there are 4 equal area rectangles. thus AB= AP+PB = 57+6 = 63 inches.

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Re: The figure above shows the dimensions of a rectangular board
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24 Mar 2016, 08:47

VeritasPrepKarishma wrote:

milind1979 wrote:

Attachment:

ps4.JPG

The length of the rectangle is 240 inches. The diagram shows you the isosceles triangle whose side will be 6 inches. From 240, if we remove 2 of these sides of 6 inches each, we will be left with 228 inches.

Attachment:

Ques.jpg

This 228 inches has to be equally divided into 4 parts as shown by the blue arrows. Why are these parts equal? Because the question says that the four pieces are identical. So the smaller side of each piece has to be equal (Look at the blue line on the top. This should be equal to the blue lines at the bottom).

The length of each of the blue lines will be 228/4 = 57 inches.The length of AB = 57 + 6 inches = 63 inches.

Simply loved your explanation, short and crisp. No unnecessary formulae, simple common sense. I envy you, for the thought didn't strike me. I solved it but in a lengthy way. Thank you. It's a moment of qualia for me.
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Re: The figure above shows the dimensions of a rectangular board
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01 Jul 2018, 13:19

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